Device and method for sub-band decomposition of image signals

ABSTRACT

The present invention relates to a device and method for sub-band decomposition of an image signal (S), that includes a cascade with n sequential median filters (M 1,  M 2,  M 3,  M 4 ) where n≧2, each having an input and an output, with the image signal (S) being fed to the input of a first median filter (M 1 ) and the input of each median filter (M 2,  M 3,  M 4 ) following the first median filter (M 1 ) being connected to the output of the previous median filter (M 1,  M 2,  M 3 ) in the cascade, and at least one linking element (SUB 1,  SUB 2,  SUB 3,  SUB 4 ) having at least two inputs and one output, where one output signal of one of the median filters (M 1,  M 2,  M 3,  M 4 ) or the image signal (S) is fed to each of the inputs and where a sub-signal (S 1,  S 2,  S 3,  S 4 ) is available at the output.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a device and method for sub-banddecomposition of image signals.

[0002] Many methods used for local noise reduction are based on theadaptive application of linear local operators to the individual pixelsor the signal values of the pixels. Such methods are described by Le, J.S., in the article entitled “Digital Image Smoothing and the SigmaFilter”, Computer Vision Graphics Image Processing, Vol. 24, pp.255-269, 1983; in the publication by Tekalp, M. A., entitled “DigitalVideo Processing”, Prentice-Hall, 1995; by de Haan, G., T. G.Kwaaitsaal-Spassova, M. Larragy, and O. A. Ojo, in the article entitled“Memory Integrated Noise Reduction IC for Television”, IEEE Trans. onConsumer Electronics, Vol. 42, No. 2, pp. 175-181, May 1996; and bySchröder, H. and H. Blume in the publication entitled “MehrdimensionaleSignalverarbeitung [Multidimensional Signal Processing]”, Vol. 2, B. G.Teubner, 2000 for example. This principle of applying linear localoperators to individual pixels can be combined only to a limited degreewith the image model present (problems occur in particular at the edgesof the image) so that the efficiency of this method is limited.

[0003] The method described by Lebowski, F. in the publication entitled“Bildschärfeverbesserung von hochaufgelösten Festbildern [ImageDefinition Improvement in Still Images]”, VDI Verlag, 1993 useshierarchical stepwise processing in which threshold values depending onthe frequency proportions are set in the signal to control noisereduction.

[0004] There are also methods based on sub-band decomposition of theimage signal followed by processing of the sub-bands. In past years manypapers have centered on the design of appropriate sub-band decompositionmethods. The linear decomposition methods include simple linearseparating filters, described by Rossi, J. P., in the publication“Digital Technique for Reducing Television Noise”, SMPTE Journal, Vol.87, pp. 134-105, March, 1978; there are also pyramid decompositionmethods described by Burt, P. J. and E. H. Adelson, in the publication“The Laplacian Pyramid as a Compact Image Code”, IEEE Trans. onCommunications, Vol. 31, pp. 532-540, 1983, and methods based on waveletdecomposition of the signal.

[0005] However, linear decomposition methods have only limitedusefulness for noise reduction in image signals because of theirproperties in the edge area. The goal of sub-band decomposition isextraction or filtering out of image elements and features with specialproperties. When band splitting occurs, the use of linear filters leadsto sub-bands that differ in the frequency components they contain. Thistype of signal splitting is cumbersome, particularly in the case ofsub-band decomposition for noise reduction, as typical image contentsconsist of a great many edges as well as other elements, and these edgesin turn are composed of many different frequency components. The resultis that the signal components of an edge enter many different bands,making it difficult to distinguish between noise and signal components.Because of this, either no noise reduction is accomplished in the edgearea or signal components of the edge are recognized as noise and areaccordingly removed from the signal.

[0006] These problems do not occur in nonlinear sub-band decompositionin which the edges of an image signal are not broken down into manysmall portions but stay together in one sub-band. Such nonlinearsub-band decomposition using a filter bank with median filters isdescribed for example in by Salembier, P. and M. Kunt, in thepublication “Size-sensitive Multiresolution Decomposition of Images withRank Order Based Filters. Signal Processing”, Vol. 27, No. 2, pp.205-241, 1992 and explained further with reference to FIG. 1. The basicdesign and function of a median filter is described for example byHelmut Schönfelder, in the publication “Digitale Filter in derVideotechnik [Digital Filters in Video Technology]”, Drei-R-Verlag,Berlin, 1988, pp. 125-127. Quadratic median filters for image processingare described for example by Rosenfeld, Kak, in “Digital PictureProcessing”, Academic Press, Inc., 2^(nd) edition, 1982, pp. 261-263.

[0007] The filter shown in FIG. 1 has K quadratic median filters ofincreasing sizes, to each of which the image signal S(x, y) is fed. TheK median filters have different filter lengths or filter sizes so that,when determining the output signal value of a given pixel, they considerthe signal values of different numbers of pixels from the environment ofthe given pixel. The filter length and filter size increase with thenumber K of median filters used.

[0008] At the output of the filter, K+1 signals are available,corresponding to decomposition of the image signal into K+1 sub-bands.These K+1 signals comprise the output signal of the K-th median filter,difference signals formed from the output signals of the adjacent medianfilters, and a difference signal formed from the original image signaland the output signal of the first median filter.

[0009] The signal at the output of each of the median filters ischaracterized in that it contains the original image signal in whichimage features with half the size of the median filter are suppressed.In addition, the noise output in the image signal is reduced by the useof median filters. For the filter shown in FIG. 1, this means that thesignals at the output of the median filters contain fewer and fewerimage features as K increases and are increasingly free of noise.Formation of the difference of the output signals of the median filtersthus leads to output signals of the total filter that contain only imagefeatures that can just pass the smaller of the two median filters fromwhose output signals a difference signal is formed but which are alreadysuppressed by the larger of the two median filters. The output signalsof the total filter also contain noise portions, which contribute inthis size range, but which are strongly limited in their amplitude.

[0010] In summary, at the output of the filter illustrated in FIG. 1 aresignals that each represent a sub-band of the frequency spectrum of theimage signal and that each correspond to image elements of differentsizes and still have noise components with a low amplitude when theimage signal is noisy.

[0011] The disadvantage of the band splitting shown in FIG. 1 usingparallel median filters of different lengths is that the size of thefilter mask increases with the number K of median filters, namely withthe number of stages. It has been proposed for example that the size ofa quadratic filter mask be allowed to increase exponentially with thenumber of stages. However this makes determination of the median valuesrather expensive.

[0012] To reduce this expenditure, a proposal has been made to reducethe necessary filter size and data volume by stepwise sub-scanning ofthe signals. Non-linear pyramid decompositions are described by Cha, H.and L. F. Chaparro, in the publication “Adaptive MorphologicalRepresentation of Signals: Polynomial and Wavelet Methods”,Multidimensional Systems and Signal Processing, Vol. 8, pp. 249-271,1997, and by Donoho, D. I. and T. P. Y. Yu, in the publication entitled,“Nonlinear ‘Wavelet Transforms’ Based on Median Interpolation”, SIAMJournal on Math. Anal., Vol. 31, No. 5 which are based on median filtersand morphological operators. However, noise reduction based on pyramiddecomposition has the disadvantage that these methods are notshift-invariant so that the resulting image contains phase-dependentnoise. Moreover, a polynomial approximation is proposed in the citedreferences for synthesis of the pyramid signals, which has the sameproblems in the edge area as is the case with the linear sub-banddecomposition method.

[0013] Other methods for nonlinear sub-band decomposition that havebetter properties than linear sub-band decomposition filters in the edgearea include not only sub-band decomposition using median filters butalso wavelet decomposition with signal-adaptive lifting, described forexample by Claypoole, R. L., G. Davis, W. Sweldens, and R. Baraniuk,“Nonlinear Wavelet Transforms for Image Coding via Lifting”. Submittedto IEEE Transactions on Image Processing, 1999; by Heijmans, H. J. A. M.and J. Goutsias, in the article entitled “Nonlinear MultiresolutionSignal Decomposition Schemes: Part II: Morphological Wavelets”, IEEETrans. on Image Processing, Vol. 9, No. 11, 2000; and by Piella, G. andN. J. A. M. Heijmans, in the publication entitled “Adaptive LiftingSchemes with Perfect Reconstruction”, Research Report PNA-R0104, Centrumvoor Wiskunde en Informatica (CWI), 2001.

[0014] Because of the high expenditure and the properties of thesub-bands, these methods have limited usefulness for sub-banddecomposition, namely dividing the image signal into various sub-signalsthat represent different frequency bands of the image signal.

[0015] Therefore, there is a need for an improved device and a methodfor sub-band decomposition of image signals.

SUMMARY OF THE INVENTION

[0016] An aspect of the invention is based on cascading of medianfilters. A device according to an aspect of the invention has a cascadewith n sequential median filters, each of which has an input and anoutput, where n≧2 and where the image signal is fed to the input of afirst median filter and where the input of each median filter followingthe first median filter is connected to the output of the previousmedian filter in the cascade. To form sub-band signals from outputsignals of the median filter, linking elements are present, each ofwhich has two inputs and one output, where an output signal of one ofthe median filters or the image signal is fed to each of the inputs andwhere a sub-band signal is available at the output.

[0017] In one embodiment, n linking elements are present; the imagesignal is fed to a first linking element and an output signal of a firstmedian filter and output signals from two median filters each are fed tothe other linking elements. These two median filters, whose outputsignals are fed to a linking element, are, in another embodiment of theinvention, two sequential median filters in the cascade.

[0018] The linking elements are preferably subtracters that subtract theoutput signal of the first filter from the image signal and the outputsignal of a median filter from the output signal of another medianfilter previous to it in the cascade to form sub-band signals.

[0019] As well as the output signals of the n subtracters, the lastmedian filter also delivers a sub-band signal in the cascade, so thatwith an arrangement with n median filters and n subtracters, n+1sub-band signals can be produced.

[0020] As known and explained for example in by Helmut Schönfelder, inthe publication “Digitale Filter in der Videotechnik [Digital Filters inVideo Technology]”, Drei-R-Verlag, Berlin, 1988, pp. 125-127 and byRosenfeld, Kak in the publication “Digital Picture Processing”, AcademicPress, Inc., 2^(nd) edition, 1982, pp. 261-263, in a median filter forforming a filter output signal value for a pixel, as well as the inputsignal value of this pixel the signal values of other pixels are takeninto consideration, with the signal values being sorted by size and theaverage signal value of the sorted signal value sequence being output asthe filter output value. Median filters have the property that edgeprogressions in an image remain after the image signal has been filteredwith a median filter, but without image features, meaning that delimitedimage areas can be masked out (i.e., “filtered out”) depending on thefilter size. Here, the filter size denotes the number of signal valuestaken into consideration upon filtering.

[0021] In one embodiment, the median filters are designed in such a waythat when an output value is determined for a pixel, not only the inputsignal value for this pixel but also input values of pixels disposed ina cruciform arrangement around this pixel are taken into consideration,with the axes of the cross extending from the pixel in the horizontaland vertical directions on both sides of the pixel. Consideration onlyof input values of pixels that lie on the axes of a cross instead ofconsideration of all the pixels that lie for example in a square or acircle around a particular pixel reduces the cost of implementing thefilter and the computing burden. Of course, in the context of theinvention median filters can be used that consider the pixels that liein an annular arrangement around the pixel for which a filter outputvalue is calculated.

[0022] With the cascading according to the invention it is possible,when producing a filter output value for a given pixel, for the medianfilters to consider the signal values of pixels whose distance from thegiven pixel differs from filter to filter. In this way, image featuresof different sizes can be filtered in the individual filter stages.

[0023] In one embodiment in which the pixels taken into considerationare disposed in a cross around a given pixel, the cascading according tothe invention makes it possible, when producing a filter output valuefor a given pixel, for the median filters to consider the signal valuesof pixels whose distance in the vertical and horizontal directions fromthe given pixel differs from filter to filter without however increasingthe computing burden and expense when implementing the median filterfrom filter to filter in the cascade. Thus, in one embodiment of theinvention, as well as the input signal value of a given pixel, thesignal values of four pixels are taken into consideration, said fourpixels lying on the axes of a cross whose point of intersection is atthe given pixel and which extend for equal distances from the givenpixel in the four axial directions.

[0024] In this case the distance of the pixels taken into consideration,which are disposed symmetrically around the given pixel, increases fromfilter to filter in the cascade.

[0025] Each of these median filters attenuates image features withspecific dimensions, with these dimensions being dependent on thedistance of the pixels considered by the median filters from the givenpixel. The cascaded median filters are so constructed that the size ofthe image features filtered out through the individual median filtersincreases from filter to filter in the cascade. Since an output signalof a previous median filter in the cascade is fed to each median filter,with the exception of the first median filter in the cascade, thesemedian filters receive input signals in which the image featuresfiltered out by the previous median filters are no longer retained. Eachmedian filter in the cascade thus has to be designed to filter out onlyimage features with a specific size, which reduces the number of pixelsto be taken into consideration in median filtering, as described.

[0026] For forming the difference between output signals of sequentialmedian filters, sub-band signals are produced that contain only thoseimage features that can still pass through a filter in the cascade andare filtered out by a filter that follows this filter in the sequence.

[0027] In the embodiment in which the same number of signal values—ofpixels with distances from a given pixel that differ from filter tofilter—are used for forming an output signal value in the individualmedian filters, the image signal can be analyzed by the device accordingto the invention in terms of image features with different sizes withouthaving to increase expenditure in the individual stages/median filtersof the cascade. The size of the different image features that can beanalyzed depends on the number of median filters in the cascade. Thedevice according to the invention brings about band splitting of theimage signal on the basis of cascaded and weighted median filters, withthe sub-bands having comparable properties. Signal portions with a sizecorresponding to the number of stages are separated in the sub-bands inquestion.

[0028] The device according to the invention for sub-band decompositionis particularly suitable for noise suppression in image signals. Forthis purpose, the sub-band signals are fed to noise suppression units,and output signals from these noise suppression units are added to forma noise-suppressed image signal.

[0029] Noise suppression is accomplished for example by noisesuppression devices that implement a softcoring characteristic, in whichsignals with an amplitude lying within a given interval are suppressedwhile other signal values pass through the noise suppression device.

[0030] Sub-band decomposition by the device according to the inventionleads to signals that, in addition to noise, still contain signalportions of image elements whose size corresponds to the individualmedian filter dimensions. The fact that with this type of band splittingthe image elements can no longer be divided into several sub-bands inlinear band splitting, but remain largely in just one band with fulledge steepness, allows simple distinction between useful signals andnoise, based on signal amplitude. Moreover, the signals of the sub-bandsin areas where there is no signal portion have an expected value ofzero. As a result, noise reduction can be simply accomplished by a noisesuppression device with a coring characteristic.

[0031] These and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of preferred embodiments thereof, as illustrated in theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWING

[0032]FIG. 1 is a prior art device for sub-band decomposition;

[0033]FIG. 2 is a device for sub-band decomposition with cascaded medianfilters;

[0034]FIG. 3 is a rectangular section of an image area;

[0035]FIG. 4 shows the coefficients of the individual median filters inthe cascade based on a weighting matrix;

[0036]FIG. 5 shows a device for noise suppression in an image signalthat has a device for sub-band decomposition and noise suppressionunits, to which sub-band signals are fed; and

[0037]FIG. 6 is the curve of a noise suppression unit according to FIG.5.

DETAILED DESCRIPTION OF THE INVENTION

[0038]FIG. 2 shows one example of a device according to the inventionfor sub-band decomposition of an image signal S(x,y). The device shownhas a cascade with n median filters M1, M2, M3, with n=3 in the sampleshown. The median filters M1, M2, M3 each have an input and an output.The image signal S(x,y) is fed to a first median filter M1. The inputsof the median filters M2, M3 following the first median filter are eachconnected at the output of the previous median filter M1, M2, so that anoutput signal F1(x,y) of the first median filter is fed to the input ofthe second median filter M2 and an output signal F2(x,y) of the secondmedian filter M2 is fed to the input of the third median filter M3.

[0039] The device shown also has in the example n=3 subtracters SUB1,SUB2, SUB3, each of which has two inputs and one output, withsub-signals T1(x,y), T2(x,y), T3(x,y) applied to the outputs ofsubtracters SUB1, SUB2, SUB3. Another sub-band signal T4(x,y) isavailable at the output of the last median filter M3 in the cascade. Afirst subtracter SUB1 forms the first sub-band signal T1(x,y) from thedifference of image signal S(x,y) and the output signal F1(x,y) of thefirst median filter M1. The sub-band signals T2(x,y), T3(x,y) are formedcorrespondingly from the differences of output signals F1(x,y), F2(x,y),F3(x,y) of two sequential median filters M1, M2, M3.

[0040] The operation of a median filter will now be briefly describedwith reference to a rectangular section of an image shown in FIG. 3. Theimage is made of a plurality of pixels determined by their coordinatesin the horizontal direction (x direction) and in the vertical direction(y direction) and to each of which a signal value is assigned. Thissignal value can have a brightness value or a chrominance value. Theimage signal S(x,y) contains a sequence of signal values of thesepixels; the image signal can be a luminance signal that contains thebrightness value or a chrominance signal that contains the chrominancevalue.

[0041] For each signal value S(x₀,y₀) of any given pixel (x₀,y₀) themedian filter generates a filter output value where, in addition to thesignal value S(x₀,y₀) of this pixel (x₀,y₀), adjacent pixelsS(x₀±a,y₀±b), a and b being integers, are considered in the formation ofthe output value. The median filter sorts the signal values of thepixels considered by size and outputs the average of the size-sortedsignal values as the output values.

[0042] As will be further described below, the cascade arrangementenables median filters to be used that consider not only the signalvalue of pixel (x₀,y₀) but also other pixels whose distance from pixel(x₀,y₀) increases from filter to filter.

[0043] In one embodiment, median filters are used that when an outputvalue for a given pixel (x₀,y₀) is generated, as well as the signalvalue S(x₀,y₀) of this pixel consider only those pixels that arise froma cruciform pixel arrangement around pixel (x₀,y₀), namely the signalvalues for pixels that lie on two straight lines passing through pixel(x₀,y₀), these lines in particular being a horizontal line with pixels(x₀±a,y₀) and a vertical line with pixels (x₀,y₀±b).

[0044] In one embodiment, only four additional pixels are consideredthat are the same distance from the pixel on the axes of the cruciformarrangement, with the distance of the pixels considered from pixel(x₀,y₀) differing from filter to filter and increasing from filter tofilter starting at the first median filter M1 to which the image signalis fed.

[0045] With reference to FIG. 4, examples of weighting matrices of themedian filters will be explained in a cascade according to the inventionof median filters, as shown for example in FIGS. 2 and 5.

[0046] A weighting matrix in the present case generally indicates thepixels whose signal values should be considered in median filtering andhow the signal values of these pixels are to be weighted beforefiltering, that is, before the size-sorting.

[0047] In the example shown in FIG. 4, the matrices have only at theouter ends of a cruciform arrangement weighting factors that arenon-zero, namely, only pixels of a cruciform arrangement are consideredin filtering that have weighting factors of zero outside the cross. Theweighting factor at the intersection represents the weighting of thesignal value of a given pixel, for example of pixel (x₀,y₀) according toFIG. 3, for which a filter output value is generated. The remainingweighting factors represent the weighting factors for other pixelsconsidered in median filtering.

[0048] The first median filter M1 with a filter matrix according to FIG.4 considers, when forming the output value, not only the signal value ofa pixel (x₀,y₀) but also signal values of pixels (x₀+1,y₀), (x₀−1,y₀),(x₀,y₀+1), and (x₀,y₀−1), namely signal values removed by one pixel onthe axes from the pixel (x₀,y₀) in question.

[0049] If the signal value of point (x₀y₀) is distinguished from thesignal values of the pixels surrounding it, namely pixels(x₀+1,y₀),(x₀−1,y₀), (x₀,y₀+1), and (x₀,y₀−1), the signal value of pixel(x₀, y₀) in the output signal is replaced by the signal value of one ofthe pixels (x₀+1,y₀), (x₀−1,y₀), (x₀,y₀+1), and (x₀,y₀−1) by medianfiltering. An image feature—that is an image area of delimited sizedistinguished from the environment—that covers only one pixel, is thussuppressed or filtered out by the first median filter, while imagefeatures larger than the size of one pixel are not filtered out.

[0050] The first sub-band signal T1(x,y) according to FIG. 2 formed fromthe difference of the image signal S(x,y) and the first filter signalF1(x,y) thus contains image features the size of one pixel, while thesignal portions of larger image features that are also still containedin the first filter signal F1(x,y) are distinguished by differenceformation.

[0051] The second median filter M2 considers, when forming the outputvalue, not only the signal value of a given pixel (x₀,y₀), but alsosignal values of pixels (x₀+2, y₀), (x₀−2, y₀), (x₀, y₀+2), and (x₀,y₀−2), namely signal values that are two pixels distant from the pixel(x₀,y₀) on the axes. This second median filter M2 filters out imagefeatures that have a vertical and horizontal size of two or fewerpixels. The second sub-band signal T2(x,y) that according to FIG. 2 isformed from the difference of the first filter signal F1(x,y) and thesecond filter signal F2(x,y) thus contains image features that are thesize of two pixels, while the signal portions of larger image featuresthat are still contained in both the first and in the second filtersignal F1(x,y) are distinguished by difference formation. Image featureswith a size of only one pixel are not contained in the second sub-bandsignal T2(x,y) as these have already been filtered out by the firstmedian filter.

[0052] The third median filter M3 considers, when forming the outputvalue, not only the signal value of a given pixel (x₀,y₀), but alsosignal values of pixels (x₀+3, y₀), (x₀−3, y₀), (x₀, y₀+3), and (x₀,y₀−3), namely signal values that are three pixels distant from the givenpixel (x₀,y₀) on the axes, and the fourth median filter M4 considers,when forming the output value, not only the signal value of a givenpixel (x₀,y₀), but also signal values of pixels (x₀+4, y₀), (x₀−4, y₀),(x₀, y₀+4), and (x₀, y₀−4), namely signal values that are four pixelsdistant from the given pixel (x₀,y₀) on the axes. Thus, the third medianfilter filters out image features that have a vertical and horizontalsize of three pixels or fewer, and the fourth median filter filters outimage features that have a vertical and horizontal size of four pixelsor fewer. The third sub-band signal T3(x,y) formed from the differenceof the second filter signal F2(x,y) and the third filter signal F3(x,y)thus contains image features as large as three pixels, while the signalportions of larger image features that are still contained both in thefirst and in the second filter signal F2(x,y) are distinguished bydifference formation. Image details smaller than three pixels are notcontained in the third sub-band signal T3(x,y) as these have alreadybeen filtered out by the previous median filters M1, M2 in the cascade.

[0053] Correspondingly, a fourth sub-band signal contains image featuresthe size of four pixels, while the signal portions of larger imagefeatures are distinguished by difference formation. Image featuressmaller than four pixels are not contained in the fourth sub-band signalas these have already been filtered out by the previous median filtersM1, M2, M3 in the cascade.

[0054] All the image features larger than over three or four pixels arecontained in the output signal of the last median filter, of filter M3in FIG. 2 and of filter M4 in FIG. 5, which is output as a sub-bandsignal. In general, in a cascade with n median filters, n+1 sub-bandsignals can be generated, each of which contains image features with aspecific size; in order to reduce the computing burden, each medianfilter considers not only the signal value S(x₀,y₀) of a given pixel(x₀,y₀), but also preferably the signal values of only four other pixels(x₀+k,y₀), (x₀−k,y₀), (x₀,y₀+k), and (x₀,y₀−k), where k is an integerand the distance k from two sequential median filters preferably differsby one. The size of the image features suppressed by the filter inquestion is then k. The distance of the pixels considered by medianfiltering from the pixel for which a filter output value was determinedin the filtering step in question increases from filter to filterpreferably by one pixel, so that the image features filtered out fromfilter to filter differ in dimensions by one pixel each.

[0055] Based on the difference formation between two filter outputsignals, to form a sub-band signal, each sub-band signal contains onlythose image features that still pass through a filter in the cascade andare filtered out by the next filter in the cascade.

[0056] One embodiment provides that, the pixel values considered inmedian filtering when generating the output signal are differentlyweighted before size-sorting. Thus, the signal value of the centralpixel (x₀,y₀) is more strongly weighted than the surrounding pixels(x₀+k,y₀), (x₀−k,y₀), (x₀,y₀+k), and (x₀,y₀−k).

[0057] The cascading of the median filters makes it possible for theindividual median filters to be designed only for filtering those imagefeatures that are still contained in the filter input signal and havenot yet been filtered out by the previous median filters. This reducesthe circuitry burden or computing burden for the individual filters andmakes it possible to use weighting matrices in which the distance of thepixels considered increases from filter to filter in the cascadestarting from the first filter M1 without increasing the number ofpixels considered in the cruciform arrangement according to FIG. 4.

[0058] Of course, any additional weighting matrices can be used in whichthe distance of the pixels considered in median filtering from the givenpixel increases from filter to filter. As well as pixels lying on across with horizontal and vertical axes as shown in FIG. 4, the pixelscan lie in any position in a cruciform arrangement, for example on adiagonal cross; with a diagonal cross, as well as the signal value ofthe pixel (x₀,y₀), signal values of pixels (x₀+k,y₀+k), (x₀+k,y₀−k),(x₀−k,y₀+k), and (x₀−k,y₀−k) are considered.

[0059] Furthermore, the pixels considered in median filtering can alsobe disposed annularly around the pixel (x₀,y₀), in which case the ringcan have any shape (particularly approximately round or rectangular) andwhere the distance of the ring from the pixel (x₀,y₀) for which a filteroutput value is determined increases from filter to filter. In thisembodiment, the number of pixels considered increases from filter tofilter because the size of the ring increases.

[0060] The device according to the invention that brings about splittingof the image signal into sub-band signals containing image features withdifferent resolutions is particularly suitable for use in a device fornoise suppression. Such a device is shown in FIG. 5.

[0061] The device has a cascade with n=4 median filters M1, M2, M3, M4,which in particular can have a weighting matrix of the type describedabove. The filter output signals F1, F2, F3, R4 formed by differenceformation or difference formation of the first filter output signal F1and the sub-band signals T1(x,y), T2(x,y), T3(x,y), and T4(x,y)containing image signal S are fed in this device to noise suppressionunits R1, R2, R3, R4 at whose outputs noise-suppressed sub-band signalsT1′(x,y), T2′(x,y), T3′(x,y), and T4′(x,y) are applied, which are addedup and added to the filter output signal F4(x,y) of the last medianfilter in the cascade to produce a noise-suppressed image signalS′(x,y).

[0062] The noise suppression units R1, R2, R3, R4 have for example atransfer curve with the shape shown in FIG. 6. Here, for an outputsignal g(x) we have: ${g(x)} = \left\{ \begin{matrix}{x - x_{c}} & {{\text{for}\quad x} > x_{c}} \\0 & {{\text{for}\quad - x_{c}} \leq x \leq x_{c}} \\{x + x_{c}} & {{\text{for}\quad x} < x_{c}}\end{matrix} \right.$

[0063] Signals with an amplitude less than x_(c) are thus suppressed asthey are assumed to be noise signals.

[0064] This noise suppression technique is particularly effective forthe sub-band signals that are obtained by the device for sub-banddecomposition. The sub-band decomposition then leads to signals thatcontain not only noise but also signal portions of image elements/imagefeatures whose size corresponds to the median filter sizes in question,namely the distance between the central pixel (x₀,y₀) and the pixelsalso taken into consideration. The fact that, by this type of bandsplitting, the image elements are no longer divided up into multiplesub-bands as in the case of linear band splitting but largely remain injust one band with full edge steepness makes it easy to distinguishbetween useful signals and noise based on the signal amplitude.Moreover, the signals of the sub-bands in areas where there is no signalportion have an expected value of zero. As a result, noise suppressioncan be accomplished by using a so-called coring characteristic, as shownin FIG. 6. Research in this connection has shown that the use of asoftcoring characteristic with softcoring gives very good results. Thechoice of the threshold value x_(c) is governed by the scatter in theindividual sub-bands. Here, the threshold values should not exceed twicethe value of the noise scatter in the corresponding band. Noisereduction is achieved by (particularly) the noise components in thedifference bands having small signal amplitudes while the image elementswith this type of splitting have large amplitudes.

[0065] To summarize, the device according to an aspect of the inventionmakes effective sub-band decomposition possible at relatively low cost.The reduction in expenditure for determining the output values of theindividual median filters in the cascade is achieved by having theindividual median filter stages consider as few input values as possibleby appropriate weighting, as explained above.

[0066] Of course, any other median filters that are orthogonal to eachother can be used as median filters, in which the previous medianfilters in the cascade pass signal portions that are filtered out onlyby a following filter in the cascade.

[0067] The cascading of the median filters makes it possible for theindividual median filters to be designed only for filtering those imagefeatures that are definitely still contained in the filter input signal,namely that have not yet been filtered out by the previous medianfilters. This reduces the circuitry burden or computing burden for theindividual filters.

[0068] Although the present invention has been shown and described withrespect to several preferred embodiments thereof, various changes,omissions and additions to the form and detail thereof, may be madetherein, without departing from the spirit and scope of the invention.

What is claimed is:
 1. Device for sub-band decomposition of an imagesignal (S), comprising: a cascade with n sequential median filters (M1,M2, M3, M4) where n≧2, each having an input and an output, with theimage signal (S) being fed to the input of a first median filter (M1)and the input of each median filter (M2, M3, M4) following the firstmedian filter (M1) being connected to the output of the previous medianfilter (M1, M2, M3) in the cascade, at least one linking element (SUB1,SUB2, SUB3, SUB4) having at least two inputs and one output, where oneoutput signal of one of the median filters (M1, M2, M3, M4) or the imagesignal (S) is fed to each of the inputs and where a sub-signal (S1, S2,S3, S4) is available at the output.
 2. Device according to claim 1having n linking elements (SUB1, SUB2, SUB3, SUB4), with the imagesignal (S) and one output signal of a median filter (M1) being fed to alinking element (SUB1) and the output signals (F1, F2, F3, F4) from twomedian filters (M2, M3, M4) being fed to the other linking elements(SUB2, SUB3, SUB4).
 3. Device according to claim 2 in which the outputsignals (F1, F2, F3, F4) from two sequential median filters (M2, M3, M4)are fed to the linking elements.
 4. Device according to claim 3 in whichthe linking elements (SUB1, SUB2, SUB3, SUB4) are formed as subtracters.5. Device according to claim 4, in which n+1 sub-band signals (T1, T2,T3, T4, T5) are available, each being formed in the cascade by outputsignals of the linking elements (SUB1, SUB2, SUB3, SUB4) and the filteroutput signal (F3; F4) of the last median filter (M3; M4).
 6. Deviceaccording to claim 5, in which the median filters (M1, M2, M3, M4) areeach designed so that, when determining a filter output value for agiven pixel (x₀,y₀), they consider not only one filter input valueS(x₀,y₀) for this pixel (x₀,y₀) but also input values of pixels that aredisposed around this given pixel (x₀,y₀).
 7. Device according to claim 6in which a distance between the pixels considered and pixel (x₀,y₀)increases from median filter to median filter in the cascade.
 8. Deviceaccording to claim 5, in which the median filters (M1, M2, M3, M4) areeach designed so that, when determining a filter output value for agiven pixel (x₀,y₀), they consider not only one filter input valueS(x₀,y₀) for this pixel (x₀,y₀) but also the input values of pixelsdisposed in a cruciform arrangement around this given pixel.
 9. Deviceaccording to claim 8 in which the pixels whose signal values areconsidered in addition to the filter input value S(x₀,y₀) for the givenpixel (x₀,y₀) for forming the filter output value for the pixel (x₀,y₀)are at a distance from pixel (x₀,y₀) that differs from filter to filterfor the individual median filters (M1, M2, M3 M4) in the horizontal andvertical directions.
 10. Device according to claim 9, in which the pixeldistance for sequential median filters (M1, M2, M3, M4) increasesstarting at the first median filter (M1).
 11. Device according to claim10, in which the median filters consider the same number of signalvalues of pixels in determining a filter output value for a given pixel(x₀,y₀).
 12. Device according to claim 10 in which the median filtersconsider not only the filter input value S(x₀,y₀) of a pixel (x₀,y₀) butalso the signal values of four other pixels (x₀+k,y₀), (x₀−k,y₀),(x₀,y₀+k), and (x₀,y₀−k) which, in a cruciform arrangement, are at thesame distance from pixel (x₀,y₀) in the horizontal and the verticaldirection.
 13. Device for noise suppression in image signals that has adevice for sub-band decomposition according to claim 10, in which atleast some of the sub-band signals (T1, T2, T3, T4) are fed to noisesuppression units (R1, R2, R3, R4) and in which output signals from thenoise suppression units (R1, R2, R3, R4) are added to form an outputsignal (S′).
 14. Method for sub-band decomposition of an image signal,comprising: filtering the image signal (S) with an n cascaded medianfilters (M1, M2, M3, M4) where n≧2, in which the image signal (S) isfiltered by a first median filter (M1) and in which filter outputsignals (F1, F2, F3, F4) from n−1 median filters (M1, M2, M3) arefiltered by a following median filter (M2, M3, M4); and generating atleast one sub-band signal (T1, T2, T3, T4) by linking the image signal(S) with at least one filter output signal (F1) and/or by linking atleast two filter output signals (F1, F2, F3, F4).
 15. Method accordingto claim 14 in which the image signal (S) and an output signal of amedian filter (M1) are linked to a sub-band signal (T1) and in whichfilter output signals (F1, F2, F3, F4) from at least two median filters(M1, M2, M3, M4) are linked to sub-band signals (T1, T2, T3, T4). 16.Method according to claim 15 in which the output signals (F1, F2, F3,F4) from at least two sequential median filters (M2, M3, M4) are linkedto sub-band signals (T2, T3, T4).
 17. Method according to claim 16 inwhich the output signal (F1) of the first median filter (M1) issubtracted from the image signal (S) to form a first sub-band signal(T1) and in which filter output signals (F1, F2, F3, F4) of sequentialmedian filters (M1, M2, M3, M4) are subtracted from each other to formsub-band signals (T2, T3, T4).
 18. Method according to claim 17, inwhich n+1 sub-band signals (T1, T2, T3, T4, T5) are formed from theimage signal and from the filter output signals (F1, F2, F3, F4). 19.Method according to claim 18 in which the median filters (M1, M2, M3,M4) are each designed so that, when determining a filter output valuefor a given pixel (x₀,y₀), they consider not only one filter input valueS(x₀,y₀) for this pixel (x₀,y₀) but also input values of pixels that aredisposed around this given pixel (x₀,y₀).
 20. Method according to claim19 in which a distance between the pixels considered and pixel (x₀,y₀)increases from median filter to median filter in the cascade.
 21. Deviceaccording to claim 20 in which the median filters (M1, M2, M3, M4) areeach designed so that, when determining a filter output value for agiven pixel (x₀,y₀), they consider not only one filter input valueS(x₀,y₀) for this pixel (x₀,y₀) but also the input values of pixelsdisposed in a cruciform arrangement around this given pixel (x₀,y₀). 22.Device according to claim 21 in which the pixels whose signal values areconsidered in addition to the filter input value S(x₀,y₀) for the givenpixel (x₀,y₀) for forming the filter output value for the pixel (x₀,y₀)are at a distance from pixel (x₀,y₀) that differs from filter to filterfor the individual median filters (M1, M2, M3 M4) in the horizontal andvertical directions.
 23. Device according to claim 22 in which the pixeldistance for sequential median filters (M1, M2, M3, M4) increasesstarting at the first median filter (M1).
 24. Device according to claim23, in which the median filters consider the same number of signalvalues of pixels in determining a filter output value for a given pixel(x₀,y₀).
 25. Device according to claim 24 in which the median filtersconsider not only the filter input value S(x₀,y₀) of a pixel (x₀,y₀) butalso the signal values S(x₀+k,y₀), S(x₀−k,y₀), S(x₀,y₀+k), andS(x₀,y₀−k) of four other pixels (x₀+k,y₀), (x₀−k,y₀), (x₀,y₀+k), and(x₀,y₀−k) which, in a cruciform arrangement, are at the same distancefrom pixel (x₀,y₀) in the horizontal and the vertical directions.